Math 6410 • ODE

\textbf{Problem.}
In an isolated region of the Canadian Northwest Territories, a population of white wolves,
\(x\), and one of silver foxes, \(y\), compete for survival (for each population one unit
represents 100 individuals). They have a common, limited food supply, which consists
mainly of mice. A mathematical biologist models the dynamics of the competing species by
the nonlinear system
\[
\begin{aligned}
  x' &= x-x^2-xy,\\
  y' &= \frac{3}{4}y-y^2-\frac{1}{2}xy.
\end{aligned}
\]
Can the two species survive together according to this model?